I copied this:
Fatigue is a concept in metallurgy with a very specific meaning. It is degradation of the crystalline structure of a metal. A metal object or material's fatigue limit is the amount of load it can sustain before any of this effect occurs. Some metals like aluminum technically have no fatigue limit, so the loaded areas have to be designed to give good lifespan regardless. The structural metal objects all around us (bikes, buildings, planes, cars) are designed, repaired, maintained, and/or retired and replaced to work around the fatigue properties of the material.
Carbon fiber isn't a metal and doesn't have a metal-like crystalline structure, so the metallurgical concept of fatigue doesn't apply. When its internal structure is degraded from load in any way, it's broken. It simply relies on its extremely high strength to keep that from happening. When it's momentarily very heavily loaded to the cusp of what it can sustain structurally, but doesn't break, it's fine and can do that forever. (Someone that designs or inspects carbon wings or whatever might have some more to say about that, but it's the basic principle).
Note that there's kind of a linguistic tug-of-war involved with the term fatigue as it applies to carbon fiber bikes. Fatigue by the metallurgical definition is an important consideration in the care and feeding of metal bikes and parts, which is to say most of them in the world, and so cyclists and mechanics might be grounded in the metallurgical definition and bristle at drawing an analog with the durability considerations involved with carbon fiber, because it's important to understand about carbon fiber that it plays by a different set of rules. So in that sense, using the term there is or can be argued as wrong. You can use it to try to suggest an analogous relationship with metal fatigue, but in carbon fiber's case of living in a strong broken/not-broken binary, there really isn't much of an analog. But with some other materials there might be more of an analog and suddenly it doesn't look as wrong or useless to borrow the term, and some people might be in the habit of doing that, or otherwise not care about what metallurgists have to say about the word.